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Article Dans Une Revue Journal of the Royal Statistical Society: Series B Année : 2011

Asymptotic behaviour of the posterior distribution in overfitted mixture models

Résumé

In this paper we study the asymptotic behaviour of the posterior distribution in a mixture model when the number of components in the mixture is larger than the true number of components, a situation commonly referred to as overfitted mixture. We prove in particular that quite generally the posterior distribution has a stable and interesting behaviour, since it tends to empty the extra components. This stability is achieved under some restriction on the prior, which can be used as a guideline for choosing the prior. Some simulations are presented to illustrate this behaviour.
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Dates et versions

hal-00641475 , version 1 (15-11-2011)

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Judith Rousseau, Kerrie Mengersen. Asymptotic behaviour of the posterior distribution in overfitted mixture models. Journal of the Royal Statistical Society: Series B, 2011, 73 (5), pp.689-710. ⟨10.1111/j.1467-9868.2011.00781.x⟩. ⟨hal-00641475⟩
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